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Economical Sections.


Economical Sections.—It will be seen in Fig. 384 that
half the material is incapable of resistance on account of its
location near the axis, being only affected by shear, which how-
ever, has usually but a small effect. We are therefore driven
to the conclusion that ' solid' beams are uneconomical (seen also
in the solid circle and triangle in Fig. 385). The hollow circle
and hollow rectangle are an improvement, but the best results are
obtained by distributing the material near the line of limiting
stress, and thus the well-known H section (Fig. 388) is arrived
at for wrought'iron, where/c =/t approximately, while the modified
T section (Fig. 390) is add^ted for cast iron where fc >/t.

Assuming that the vertical web is for the purpose of resisting
shear, "we may find the moment of resistance by an

Approximate Method.— The direct strength of the flanges
forms a couple whose arm may be taken as the depth from
centre to centre of the flanges (the vertical web being neglected),
Let a = area of total depth of either flange,

Moment of resistance of H section =/cach   oifta^h

whichever is the lowest value.

In cast iron j = ^ or J roughly, and the flanges must have

/c     4
areas in inverse proportion.

Exact graphical solution may also be found, and we will take
a few cases.